Salam taji thesis

MODELING ADSORPTION DATA OF HYDROCARBONS ON 13X
ZEOLITE USING THE GAUSSIAN ADSORPTION ISOTHERM MODEL
by
Salam Mazen Taji
A Thesis Presented to the Faculty of the
American University of Sharjah
College of Engineering
in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science in
Chemical Engineering
Sharjah, United Arab Emirates
January 2013

Approval Signatures
We, the undersigned, approve the Master’s Thesis of Salam Mazen Taji.
Thesis Title: Modeling Adsorption data of Hydrocarbons on 13X zeolite using the Gaussian
adsorption isotherm model.
Signature Date of Signature
___________________________ _______________
Dr. Kevin Francis Loughlin
Professor, Department of Chemical Engineering
Thesis Advisor
___________________________ _______________
Dr. Dana Abouelnasr
Associate professor, California State University, Bakersfield
Department of Chemical Engineering
Thesis Co-Advisor
___________________________ _______________
Dr. Rachid Chebbi
Professor, Department of Chemical Engineering
Thesis Committee Member
___________________________ _______________
Dr. Fawwaz Jumean
Professor, Department of Biology, Chemistry and Environment
Thesis Committee Member
___________________________ _______________
Dr. Naif Darwish
Head, Department of Chemical Engineering
___________________________ _______________
Dr. Hany El-Kadi
Associate Dean, College of Engineering
___________________________ _______________
Dr. Yousef Al-Assaf
Dean, College of Engineering
___________________________ _______________
Dr Khaled Assaleh
Director of Graduate Studies

Acknowledgements
In the name of Allah most Merciful, most Gracious.
I have been indebted in the preparation of this thesis to my advisors, Dr. Kevin Loughlin
of the American University of Sharjah, and Dr. Dana Abouelnasr of California State
University. Their patience and constant support, as well as their academic experience,
have been invaluable to me. I am extremely grateful to my committee members, Dr.
Fawwaz Jumean from the Department of Biology, Chemistry and Environment and Dr.
Rachid Chebbi from the Chemical Engineering Department for their constructive
criticism and their professional help that contributed significantly to the completion of
this work. I must also acknowledge my laboratory instructor, Engineer Essam Al-
Zubaidy for his time, technical support and the huge effort made by his side throughout
my graduate years.
My parents Dr. Mazen Taji and Dr. Samar Gheibeh have always been my continuous
source of inspiration and support of my intellectual aspirations. This thesis would not
have existed without their emotional, moral and financial support. Special thanks to my
friends and colleagues, Laura and Noha for making my years at graduate school
unforgettable.

5
Abstract
Subcritical and supercritical adsorption data available in the literature for
alkanes, alkenes and aromatics on 13X zeolite are correlated using the Gaussian
adsorption model. This model is specified by three parameters: qmax, the
saturation loading; P50, adsorption pressure at 50% of the maximum loading; and
σ, the standard deviation. A semi log plot of pressure vs. the inverse of the
Gaussian cumulative distribution function produces a linear relation with a slope
equal to the standard deviation of the isotherm and an intercept equal to the
logarithm of the pressure at 50% of the maximum loading.
The model is applied to 138 alkane isotherms, 17alkene isotherms and 44
aromatic isotherms from the literature on 13X zeolite. The isotherms are
collected from 17 different studies and fitted to the model using a pre-specified
maximum saturation loading value for the supercritical isotherms and a
calculated value using crystallographic zeolite data and the Rackett or modified
Rackett equation for the subcritical isotherms. The mean standard deviation is
found to be equal to 1 for reduced temperatures greater than 0.65 and greater
than three for reduced temperatures less than 0.65.
Plots of the pressure at 50% of the maximum loading vs. the inverse of the
temperature are constructed. The slopes of the generated lines are used to
calculate the values of the heat of adsorption at 50% loading for each species.
The values are either equal or less than the values published in literature at 0%
loadings for isotherms with a sigma value of (0.5 to 1) and are remarkably
higher for isotherms with a sigma value above 3. The Gaussian model is found
to be a better fit for supercritical data than for subcritical data especially for
reduced temperatures below 0.75 where some inconsistencies are encountered.
Keywords: Isotherm, Gaussian model, alkanes, alkenes, aromatics, 13X zeolite.

6
Table of Contents
Abstract .....................................................................................................................................5
List of Figures ...........................................................................................................................9
List of Tables...........................................................................................................................15
Nomenclature ..........................................................................................................................17
CHAPTER 1: Introduction....................................................................................................20
1.1 Background................................................................................................................20
1.1.1 Definition...........................................................................................................20
1.1.2 Classification......................................................................................................20
1.1.3 Adsorption isotherms.........................................................................................21
1.1.4 Applications.......................................................................................................24
1.1.5 Adsorbents .........................................................................................................25
1.1.6 Pelletization........................................................................................................33
1.1.7 Adsorbent selection............................................................................................33
1.1.8 Measurement techniques....................................................................................34
1.2 Literature Review.......................................................................................................37
1.3 Deliverables ...............................................................................................................39
1.4 Thesis Outline............................................................................................................40
CHAPTER 2: Theoretical Background and Model Derivation.............................................41
2.1 Adsorption Equilibrium Theory.................................................................................41
2.1.1 Langmuir theory.................................................................................................41
2.1.2 Gibbs thermodynamic theory [5].......................................................................42
2.1.3 Statistical thermodynamic theory.......................................................................44
2.1.4 Empirical isotherm equations.............................................................................45
2.2 Henry’s Law...............................................................................................................45
2.3 The Gaussian model...................................................................................................46

7
2.3.1 Model derivation................................................................................................48
2.3.2 Maximum saturation loading .............................................................................53
2.3.3 Predicting adsorption data by the Gaussian model ............................................54
2.4 Conclusion .................................................................................................................60
CHAPTER 3: Sorption of alkanes on 13X............................................................................61
3.1 Introduction................................................................................................................61
3.2 Methane......................................................................................................................64
3.3 Ethane ........................................................................................................................68
3.4 Propane ......................................................................................................................73
3.5 n-butane......................................................................................................................78
3.6 iso-butane...................................................................................................................81
3.7 n-pentane....................................................................................................................85
3.8 iso-pentane.................................................................................................................88
3.9 neo-pentane................................................................................................................92
3.10 n-Hexane................................................................................................................95
3.11 n-Heptane...............................................................................................................99
3.12 n-Octane...............................................................................................................103
3.13 iso-octane.............................................................................................................106
3.14 Discussion and Conclusion..................................................................................110
CHAPTER 4: Sorption of alkenes on 13X..........................................................................117
4.1 Introduction..............................................................................................................117
4.2 Ethylene ...................................................................................................................118
4.3 Propylene .................................................................................................................121
4.4 1- butene...................................................................................................................126
4.5 Discussion and Conclusion......................................................................................130
CHAPTER 5: Sorption of aromatics or cyclic hydrocarbons on 13X.................................133
5.1 Introduction..............................................................................................................133

8
5.2 Benzene....................................................................................................................135
5.3 Toluene ....................................................................................................................139
5.4 Mesitylene................................................................................................................143
5.5 Naphthalene .............................................................................................................147
5.6 1,2,3,5 Tetramethylbenzene.....................................................................................150
5.7 1, 3, 5-Triethylbenzene ............................................................................................154
5.8 Cyclohexane.............................................................................................................157
5.9 Discussion and Conclusion......................................................................................161
CHAPTER 6: Conclusion ...................................................................................................167
REFERENCES......................................................................................................................171
VITA .....................................................................................................................................175

9
List of Figures
Figure 1.1: The five isotherm categories according to Brunauer et al. [4]. ...................................23
Figure 1.2: Molecular sieve carbons (a) Type CMSN2 with bottlenecks near 0.5 nm formed by
coke deposition on the pore mouth; (b) Type CMSH2 formed by steam activation [6]................27
Figure 1.3: (a) secondary building units. (b) Commonly occurring polyhedral units in zeolite
framework structures [7]................................................................................................................30
Figure 1.4: Framework structures of zeolite A [7].........................................................................31
Figure 1.5: Tetrahedron [9]............................................................................................................31
Figure 1.6: Sodalite cage. [9].........................................................................................................31
Figure 1.7: Framework structures of zeolite X and Y [7]..............................................................32
Figure 1.8: Chemical structure of zeolite X and Y [9]...................................................................32
Figure 1.9: Experimental setup for volumetric measurement of pure gas adsorption equilibria
[11].................................................................................................................................................35
Figure 1.10: Experimental setup for gravimetric measurements of pure gas adsorption equilibria
using a two beam balance [11].......................................................................................................36
Figure 1.11: Experimental setup for gravimetric measurements of pure gas adsorption...............36
Figure 2.1: (a) Isotherm for methane on 5A zeolite at 194.5 K. data are from Stroud et al. [30] a
value for qmax of 9 g/100 gZ is used in calculating θ. (b) cumulative distribution function for the
standard normal distribution [27]...................................................................................................47
Figure 2.2: Linearized isotherms for methane adsorption on 5A zeolite [27]. ..............................50
Figure 2.3: Data from 24 methane isotherms overlaid on a single normalized linear isotherm [27].
.......................................................................................................................................................51
Figure 2.4: Data from 24 methane isotherms, overlaid on a single normalized isotherm graph
[27].................................................................................................................................................51
Figure 2.5: Two isotherms of methane adsorption, (194.5K from [30]and 308 K from [35]) [27].
.......................................................................................................................................................52
Figure 2.6: Experimental data for 24 isotherms, compared to prediction from Gaussian model
[27].................................................................................................................................................53
Figure 2.7: Isotherms nC1 through nC8 compared to isotherms nC10 and nC12 [38]. .....................55
Figure 2.8: Linearized isotherms for nC1 through nC8 [38]. ..........................................................56
Figure 2.9: Normalized isotherms of nC1 through nC10 [38]..........................................................56
Figure 2.10: Isotherms of n-Pentane overlaid with Gaussian isotherm model [38].......................57
Figure 2.11: Isosteres for 50% loading for nC1 through nC10 [38].................................................57

10
Figure 2.12: Heats of adsorption at 50% loading according to Table 2.2 (dark squares) [38]. .....58
Figure 2.13: Predicted isotherms of n-pentane overlaid with adsorption data [38].......................59
Figure 2.14: Isotherms for n-decane, overlaid with predicted Gaussian isotherm model [38]......60
Figure 3.1: Isotherms for methane on 13X (before screening)......................................................64
Figure 3.2: Isotherms for methane on 13X (after screening).........................................................65
Figure 3.3: Linearized isotherms for methane on 13X. .................................................................66
Figure 3.4: Sigma, the slope of the linearized isotherms, as a function of reduced temperature, for
methane..........................................................................................................................................66
Figure 3.5: log Pr50 vs. 1/Tr for methane on 13X...........................................................................67
Figure 3.6: ln P50 vs. 1/T for methane on 13X...............................................................................67
Figure 3.7: Isotherms for ethane on 13X. ......................................................................................69
Figure 3.8: Linearized isotherms for ethane on 13X at subcritical temperatures. .........................70
Figure 3.9: Linearized isotherms for ethane on 13X at supercritical temperatures. ......................70
Figure 3.10: Sigma, the slope of the linearized isotherms, as a function of reduced temperature,
for ethane on 13X...........................................................................................................................71
Figure 3.11: log Pr50 vs. 1/Tr for ethane on 13X. ...........................................................................72
Figure 3.12: ln P50 vs. 1/T for ethane on 13X................................................................................72
Figure 3.13: Isotherms of propane on 13X. ...................................................................................74
Figure 3.14: Linearized isotherms for propane on 13X at subcritical temperatures......................75
Figure 3.15: Linearized isotherms for propane on 13X at supercritical temperatures...................75
for propane on 13X........................................................................................................................76
Figure 3.17: log Pr50 vs. 1/Tr for propane on 13X..........................................................................76
Figure 3.18: ln P50 vs. 1/T for propane on 13X..............................................................................77
Figure 3.19: Isotherms for n-butane on 13X..................................................................................78
Figure 3.20: Linearized isotherms for n-butane on 13X................................................................79
Figure 3.21; Sigma, the slope of the linearized isotherms, as a function of reduced temperature,
for n-butane on 13X.......................................................................................................................79
Figure 3.22: log Pr50 vs. 1/Tr for n-butane on 13X.........................................................................80
Figure 3.23: ln P50 vs. 1/T for n-butane on 13X.............................................................................80
Figure 3.24: Isotherms for iso-butane on 13X...............................................................................82
Figure 3.25: Linearized isotherms for iso-butane on 13X. ............................................................82
for iso-butane on 13X. ...................................................................................................................83

11
Figure 3.27: log Pr50 vs. 1/Tr for iso-butane on 13X. .....................................................................83
Figure 3.28: ln P50 vs. 1/T for iso-butane on 13X..........................................................................84
Figure 3.29: Isotherms for n-pentane on 13X................................................................................85
Figure 3.30: Linearized isotherms for n-pentane on 13X. .............................................................86
for n-pentane on 13X. ....................................................................................................................86
Figure 3.32: log Pr50 vs. 1/Tr for n-pentane on 13X.......................................................................87
Figure 3.33: ln P50 vs. 1/T for n-pentane on 13X...........................................................................87
Figure 3.34: Isotherms for iso-pentane on 13X. ............................................................................89
Figure 3.35: Linearized isotherms for iso-pentane on 13X............................................................89
for iso-Pentane. ..............................................................................................................................90
Figure 3.37: log Pr50 vs. 1/Tr for iso-pentane on 13X.....................................................................90
Figure 3.38: ln P50 vs. 1/T for iso-pentane on 13X........................................................................91
Figure 3.39: Isotherms for neo-pentane on 13X. ...........................................................................92
Figure 3.40: Linearized isotherms for neo-pentane on 13X. .........................................................93
for neo-pentane on 13X. ................................................................................................................93
Figure 3.42: log Pr50 vs. 1/Tr for neo-pentane on 13X....................................................................94
Figure 3.43: ln P50 vs. 1/T for neo-pentane on 13X.......................................................................94
Figure 3.44: Isotherms for n-hexane on 13X (before screening)...................................................96
Figure 3.45: Isotherms for n-hexane on 13X (after screening)......................................................96
Figure 3.46: Linearized isotherms of n-hexane on 13X.................................................................97
for n-hexane on 13X. .....................................................................................................................97
Figure 3.48: log Pr50 vs. 1/Tr for n-hexane on 13X.........................................................................98
Figure 3.49: ln P50 vs. 1/T for n-hexane on 13X............................................................................98
Figure 3.50: Isotherms for n-heptane on 13X..............................................................................100
Figure 3.51: Linearized isotherms for n-heptane on 13X. ...........................................................101
for n-heptane on 13X. ..................................................................................................................101
Figure 3.53: log Pr50 vs. 1/Tr for n-heptane on 13X. ....................................................................102
Figure 3.54: ln P50 vs. 1/T for n-heptane on 13X.........................................................................102
Figure 3.55: Isotherms for n-octane on 13X................................................................................103

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Figure 3.56: Linearized isotherms for n-octane on 13X. .............................................................104
for n-octane on 13X. ....................................................................................................................104
Figure 3.58: log Pr50 vs. 1/Tr for n-octane on 13X. ......................................................................105
Figure 3.59: ln P50 vs. 1/T for n-octane on 13X.............................................................................105
Figure 3.60: Isotherms for iso-octane on 13X (before modification)..........................................107
Figure 3.61: Isotherms for iso-octane on 13X (after modification).............................................107
Figure 3.62: Linearized isotherms for iso-octane on 13X............................................................108
for iso-Octane on 13X..................................................................................................................108
Figure 3.64: log Pr50 vs. 1/Tr for iso-octane on 13X.....................................................................109
Figure 3.65: lnP50 vs. 1/T for iso-octane on 13X. ..........................................................................109
for all chosen alkanes marked according to species ....................................................................114
for alkanes on 5A zeolite. ............................................................................................................114
Figure 3.68: Isosteres of 50% loading for all the chosen alkanes................................................115
Figure 4.1: Isotherms for ethylene on 13X. .................................................................................118
Figure 4.2: Linearized isotherms for ethylene on 13X. ...............................................................119
ethylene on 13X...........................................................................................................................119
Figure 4.4: log Pr50 vs. 1/Tr for ethylene on 13X..........................................................................120
Figure 4.5: ln P50 vs. 1/T for ethylene on 13X. ............................................................................120
Figure 4.6: Isotherms for propylene on 13X (before screening)..................................................122
Figure 4.7: Isotherms for propylene on 13X (after screening).....................................................122
Figure 4.8: Linearized isotherms for propylene on 13X (subcritical region)...............................123
Figure 4.9: Linearized isotherms for propylene on 13X (supercritical region). ..........................124
for propylene on 13X...................................................................................................................124
Figure 4.11: log Pr50 vs. 1/Tr for propylene on 13X. ....................................................................125
Figure 4.12: ln P50 vs. 1/T for propylene on 13X.........................................................................125
Figure 4.13: Isotherms for 1-butene on 13X................................................................................127
Figure 4.14: Linearized isotherms for 1-butene on 13X..............................................................127

13
for 1-butene on 13X.....................................................................................................................128
Figure 4.16: log Pr50 vs. 1/Tr for1-butene on 13X. .......................................................................128
Figure 4.17: ln P50 vs. 1/Tfor1-butene on 13X.............................................................................129
for all chosen alkenes marked according to species. ...................................................................131
Figure 4.19: log Pr50 vs. 1/Tr for all the chosen alkenes...............................................................132
Figure 5.1: Isotherms for benzene on 13X...................................................................................135
Figure 5.2: Isotherms for benzene after deleting Zhdanov pelleted isotherm on13X..................136
Figure 5.3: Linearized isotherms for benzene on 13X.................................................................137
benzene on 13X. ..........................................................................................................................137
Figure 5.5: log Pr50 vs. 1/Tr for benzene on 13X..........................................................................138
Figure 5.6: ln P50 vs. 1/T for benzene on 13X. ............................................................................138
Figure 5.7: Isotherms for toluene on 13X....................................................................................140
Figure 5.8: Linearized isotherms for toluene on 13X..................................................................141
toluene on 13X.............................................................................................................................141
Figure 5.10: log Pr50 vs. 1/Tr for toluene on 13X. ........................................................................142
Figure 5.11: ln P50 vs. 1/T for toluene on 13X.............................................................................142
Figure 5.12: Isotherms for mesitylene on 13X. ...........................................................................143
Figure 5.13: Linearized isotherms for mesitylene on 13X...........................................................144
for mesitylene on 13X..................................................................................................................145
Figure 5.15: log Pr50 vs. 1/Tr for mesitylene on 13X....................................................................145
Figure 5.16: ln P50 vs. 1/T for mesitylene on 13X. ......................................................................146
Figure 5.17: Isotherms for naphthalene on 13X. .........................................................................147
Figure 5.18: Linearized isotherms for naphthalene on 13X.........................................................148
for naphthalene on 13X................................................................................................................148
Figure 5.20: log Pr50 vs. 1/Tr for naphthalene on 13X..................................................................149
Figure 5.21: ln P50 vs. 1/T for naphthalene on 13X. ....................................................................149
Figure 5.22: Isotherms for 1,2,3,5-tetramethylbenzene on 13X. .................................................151
Figure 5.23: Linearized isotherms for 1,2,3,5- tetramethylbenzene on 13X. ..............................151

14
for 1,2,3,5- tetramethylbenzene on 13X. .....................................................................................152
Figure 5.25: log Pr50 vs. 1/Tr for1,2,3,5- tetramethylbenzene on 13X..........................................152
Figure 5.26: ln P50 vs. 1/T for1, 2, 3, 5- tetramethylbenzene on 13X............................................153
Figure 5.27: Isotherms for 1,3,5-triethylbenzene on 13X............................................................154
Figure 5.28: Linearized isotherms for 1,3,5-triethylbenzene on 13X..........................................155
for 1,3,5 triethylbenzene on 13X. ................................................................................................155
Figure 5.30: log Pr50 vs. 1/Tr for1,3,5 triethylbenzene on 13X.....................................................156
Figure 5.31: ln P50 vs. 1/Tfor1,3,5 triethylbenzene on 13X.........................................................156
Figure 5.32: Isotherms for cyclohexane on 13X..........................................................................158
Figure 5.33: Linearized isotherms for cyclohexane on 13X........................................................158
for cyclohexane on 13X...............................................................................................................159
Figure 5.35: log Pr50 vs. 1/Tr for cyclohexane on 13X. ................................................................159
Figure 5.36: ln P50 vs. 1/T for cyclohexane on 13X.....................................................................160
for the chosen aromatics and cyclic compound marked according to species.............................163
for all chosen aromatics marked according to the study..............................................................164
Figure 5.39: log Pr50 vs. 1/Tr for all the chosen aromatics............................................................165
Figure 6.1: Data from 199 hydrocarbon isotherms, overlaid on a single normalized linear graph.
.....................................................................................................................................................170
Figure 6.2: Data from 199 hydrocarbon isotherms, overlaid on a single normalized isotherm
graph. ...........................................................................................................................................170

15
List of Tables
Table 1.1: Physical vs. chemical adsorption [3] ............................................................................21
Table 1.2: Pore sizes in typical activated carbons [7]....................................................................26
Table 1.3: Typical properties of silica gel [8]................................................................................28
Table 2.1: Adsorption studies of methane on 5A zeolite [27]. ......................................................49
Table 2.2: Heats of adsorption at 50% loading..............................................................................58
Table 3.1: Data on the adsorption of alkanes on 13X....................................................................61
Table 3.2: Values of (-ΔHads) for methane.....................................................................................68
Table 3.3: Values of (-ΔHads) for ethane on 13X. ..........................................................................73
Table 3.4: Values of (-ΔHads) for propane on 13X.........................................................................77
Table 3.5: Values of (-ΔHads) for iso-butane on 13X.....................................................................84
Table 3.6: Values of (-ΔHads) for n-pentane on 13X......................................................................88
Table 3.7: Values of (-ΔHads) for iso-pentane on 13X. ..................................................................91
Table 3.8: Values of (-ΔHads) for neo-pentane on 13X..................................................................95
Table 3.9: Values of (-ΔHads) for n-hexane on 13X.......................................................................99
Table 3.10: Values of (-ΔHads) for n-heptane on 13X..................................................................103
Table 3.11: Values of (-ΔHads) for n-octane on 13X....................................................................106
Table 3.12: Values of (-ΔHads) for iso-octane on 13X. ................................................................110
Table 3.13: Values of (-ΔHads) for the chosen alkanes.................................................................116
Table 3.14: Values of (-ΔHads) for the chosen alkanes.................................................................116
Table 4.1: Data on the adsorption of alkenes on 13X..................................................................117
Table 4.2: Values of (-ΔHads) for ethylene...................................................................................121
Table 4.3: Values of (-ΔHads) for propylene. ...............................................................................126
Table 4.4: Values of (-ΔHads) for 1-butene. .................................................................................129
Table 4.5: Values of (-ΔHads) for the chosen alkenes...................................................................132
Table 5.1: Data on the adsorption of aromatics and cyclohexane on 13X...................................133
Table 5.2: Physical properties of the chosen aromatics and cyclic compound [42]. ...................134
Table 5.3: Values of (-ΔHads) for benzene. ..................................................................................139
Table 5.4: Values of (-ΔHads) for toluene.....................................................................................143
Table 5.5: Values of (-ΔHads) for mesitylene...............................................................................146
Table 5.6: Values of (-ΔHads) for naphthalene.............................................................................150
Table 5.7: Values of (-ΔHads) for 1, 2, 3, 5- tetramethylbenzene.................................................153

16
Table 5.8: Values of (-ΔHads) for 1,3,5-triethybenzene................................................................157
Table 5.9: Values of (-ΔHads) for cyclohexane. ...........................................................................160
Table 5.10: Values of (-ΔHads) for the chosen aromatics and cyclic compound..........................166
Table 6.1: Values of (-ΔHads) and σ.............................................................................................169

17
Nomenclature
a pre-exponential factor for isostere
a amount adsorbed, mole/cc
b affinity constant, kPa-1
b0 affinity constant at some reference temperature, kPa-1
b∞ affinity constant at infinite temperature, kPa-1
c free species concentration mole/cc of gas
C constant in BET equation (Eq. 2.20)
Cμ adsorbed concentration, mole/cc solid
Cμs maximum adsorbed concentration, mole/cc solid
Ed activation energy for desorption, joule/mole
jg the internal partition function of gas phase
js internal and vibrational partition function
K, K′ Henry’s law constant (Eq. 2.21)
K0, K′0 Henry’s law constant at infinite temperature (Eq. 2.23)
k Boltzman constant (Eq. 2.15), joule/mole/K
kd rate constant for desorption, dimensionless
kd∞ rate constant for desorption at infinite temperature, dimensionless
K(T) Henry’s law constant (Eq. 2.6), g/100g Z/kPa
KH Henry’s constant, g/100g Z/kPa
M molecular weight, g/mole
n carbon number or number of moles in equation 2.5
P pressure, kPa
P0 vapor pressure, kPa
PC critical pressure, kPa
PLM log mean pressure for the entire isotherm, kPa
𝑃50 pressure at 50% loading, same value as PLM, kPa
Pr reduced pressure, dimensionless
Pr,50 reduced pressure at 50% loading, dimensionless

18
R, Rg Gas constant, joule/mole/K
Ra rate of adsorption, mole/sec
Rd rate of desorption, mole/sec
Rs rate of surface striking, mole/cm2
/s
Q heat of adsorption, joule/mole
q zeolite loading, g/100 gZ
qmax maximum zeolite loading, g/100 gZ
T temperature, K
TC critical temperature
TCAR critical adsorbate reduced temperature
Tr reduced temperature
u pair wise adsorbate-adsorbate interaction energy, joule/mole
V volume of gas adsorbed, cc
Vm volume of gas adsorbed to fill a monolayer, cc
w adsorbate-adsorbate interaction energy, joule/mole
xv mole fraction of species v.
Z standard normal probability distribution variable
z coordination number
Greek Letters
α sticking coefficient
γv activity coefficient of species v
ε adsorption energy per molecule for adsorbate-adsorbent interaction,
joule/mole
π pi or spreading pressure, joule/m3
θ fractional loading, (=q/qmax)
𝜎 standard deviation for an isotherm
σ area per unit molecule (Eq. 2.10), cm2
/mole
σ0 minimum area per unit molecule (Eq. 2.10), cm2
/mole
σv partial molar surface are of species v (Eq. 2.16)
(-∆H0) heat of adsorption at 0% loading, kcal/mole
(-∆H50) heat of adsorption at 50% loading, kcal/mole

19
∆F difference in Helmholtz free energy, joule/mole
∆H0 difference in enthalpy, joule/mole
∆U0 difference in internal energy, joule/mole
∆S difference in entropy, joule/mole/K
𝛷 cumulative distribution function
𝛷−1
inverse cumulative distribution function
ζ parameter relating to the flexibility and the symmetry of a molecule
Λ the thermal de Broglie wavelength, cm
ΛIV, ΛVI constants in equation 2.17

20
CHAPTER 1: Introduction
1.1 Background
1.1.1 Definition
The first notion of adsorption came alive as early as the 18th
century when the
uptake of gases by charcoal was first described by Scheele in 1773 and by Fontana in
1777. In 1785, Lowitz discovered that charcoal took the coloring matter out of solutions
[1]. In 1814, de Saussure carried out the first systematic investigations to measure the
adsorption of different gases on a variety of adsorbents [1]. His findings outline our basic
principles of adsorption.
According to Hill [2], “Adsorption is the preferential concentration of a species at
the interface between two phases.” When a gas comes in contact with a porous solid, it
gets taken (adsorbed) into the pores of that solid. Adsorption occurs at the surface due to
the difference in concentration of the sorbate inside the pores of the adsorbent and the gas
or vapor that holds the sorbate. Like all transport phenomena adsorption occurs in order
to achieve equilibrium.
1.1.2 Classification
It is possible to classify this process into two categories: physical adsorption
(physisorption) and chemical adsorption (chemisorption). Physical adsorption occurs due
to intermolecular forces such as Van der Waals, permanent dipole, induced dipole and
quadrupole interactions. The forces involved in chemical adsorption, on the other hand,
are the much stronger valence forces. These forces involve chemical reactions and the
transfer of electrons between the adsorbent and the adsorbate. The differences between
the two adsorption types are summarized in Table 1.1.

21
Table 1.1: Physical vs. chemical adsorption [3]
Physical adsorption Chemisorption
Low heat of adsorption
(1 to 1.5 times latent heat of evaporation).
High heat of adsorption
(> 1.5 times latent heat of evaporation).
Non specific. Highly specific.
Monolayer or multilayer. Monolayer only.
No dissociation of adsorbed species. May involve dissociation.
Only significant at relatively
low temperatures.
May occur at a wide range of temperatures.
Rapid, nonactivated, reversible. Activated, may be slow and irreversible.
No electron transfer,
polarization of sorbate may occur.
Electron transfer leading to bond formation
between sorbate and surface.
Whether adsorption is chemical or physical, it is accompanied by a decrease in
the free energy of the system undergoing adsorption which makes it a spontaneous
process. This decrease is due to the saturation of the unbalanced forces on the surface of
the adsorbent. Moreover, adsorption is accompanied with a decrease in entropy because
the adsorbed gas molecule is transformed from a three dimensional movement to being
attached rigidly or with limited movement on the surface of the adsorbent. The decrease
in the free energy and in the entropy of the adsorption process means that the heat
change in the system is also negative, according to equation 1.1. Therefore the
adsorption process in general is an exothermic process. (-ΔH) in the case of adsorption
is referred to as the heat of adsorption [3].
∆𝐻 = ∆𝐹 + 𝑇∆𝑆 1.1
1.1.3 Adsorption isotherms
When an evacuated solid is brought in contact with a gas or vapor at a certain
temperature and pressure, adsorption takes place until equilibrium is established. At this
specific temperature and pressure the amount of gas that is adsorbed is a function of the
nature of the adsorbent and the adsorbate [1]. The adsorbent’s nature is defined by its
physical structure (e.g. size, shape, surface area, pore distribution) and its chemical
constitution. While for the adsorbed gas the nature is defined by its physical and chemical
properties.

22
For a given gas per unit weight of adsorbent, the amount of gas adsorbed is a
function of the final temperature and pressure at equilibrium [1].
𝑎 = 𝑓(𝑇, 𝑃) 1.2
where a represents the amount of gas adsorbed per unit mass of adsorbent, and T and P
are the final temperature and pressure respectively. When studying adsorption, either the
temperature or the pressure is varied while keeping the other constant; however, it is
more common to keep the temperature constant and vary the pressure.
A plot of the amount adsorbed per unit weight of the adsorbent vs. the pressure of the
system at equilibrium is called the adsorption isotherm.
𝑎 = 𝑓(𝑃), 𝑇𝑖𝑠𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 1.3
while on the other hand, varying the temperature and keeping the pressure constant will
generate the adsorption isobar.
𝑎 = 𝑓(𝑇), 𝑃𝑖𝑠𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 1.4
Brunauer et al. [4] classified the adsorption isotherms into five categories. Figure
1.1 shows the five different isotherm shapes where the amount adsorbed is plotted against
the normalized pressure, P/P0, P0 being the saturation pressure at the given isotherm
temperature.
Type I is referred to as the Langmuir type adsorption. The curve reaches a
maximum saturation point where adsorption no longer occurs. This happens when the
adsorbent pore size is comparable to the molecular diameter of the sorbate causing
complete filling of the micropores and hence a definite saturation limit. Large
intermolecular attraction effects result in an isotherm of type V. Type IV isotherm is
encountered in the case where there is multilayer adsorption either on a plane surface or
on the wall of pore that is wider than the molecular diameter of the sorbate. Types II and
III are observed in adsorbents in which there is a wide range of pore sizes. With increased
loading, adsorption develops continually from monolayer to multilayer and then to pore
condensation. Capillary condensation occurs because the vapor pressure of the adsorbate
inside the pores of the adsorbent is lower than that in the bulk phase due to the capillary
forces exerted by the pore walls of the adsorbent.

23
Pores with smaller size fill first at lower pressures and as the pressure increases all of the
pores are filled with liquid at the saturation pressure. According to the capillary
condensation theory, adsorption at sufficiently high pressures is due to condensation in
the mesopores [5].
Figure 1.1: The five isotherm categories according to Brunauer et al. [4].

24
1.1.4 Applications
Besides being a natural phenomenon that is worth understanding, adsorption
found a variety of important industrial applications. The most important ones are [1]:
1. Gas purification:
a. The purification of carbon dioxide coming from fermenting vats to make it
usable for carbonated water.
b. The purification of hydrogen before catalytic hydrogenation.
c. The refining of helium.
d. The drying of air and other gases.
e. The purification of air in submarines.
f. The deodorizing of refrigerating rooms.
g. The use of adsorbents for protection in gas masks.
2. Separation and recovery of gases.
a. Separation of the rare gases.
b. Extraction of gasoline from natural gas.
c. Recovery of benzene and light oil from illuminating gas.
d. Recovery of acetone, alcohol, and butanol from the waste gases of fermenting
vats.
e. Recovery of volatile solvent vapors in dry cleaning.
f. Manufacturing of artificial silk, celluloid, rubber.
3. Catalysis.
Catalysts are microporous structures which increase the rate of the
reaction. Gases get adsorbed into the catalyst pores where they react on the
surface, form products and then desorb. Adsorption on catalysts is very complex
and unpredictable due to the non-uniform catalyst surface, that is, energy, crystal
structure and chemical composition vary from one point to another on that surface
[2].

25
1.1.5 Adsorbents
Adsorbents used in commercial separation processes must have some unique
qualities that would make the process technically effective. The porosity of the adsorbent
material is an important characteristic of its effectiveness. A highly porous adsorbent
material with a high internal volume makes it more accessible for the components being
removed. Mechanical strength and resistance to attrition especially under severe
conditions, high temperatures during regeneration, are also important measures of
effectiveness. The adsorbent must be able to preserve its adsorptive capability and
efficiency in transferring adsorbing molecules rapidly to the adsorption sites. An
important aspect also is the cost of raw materials and the methods of producing the
adsorbent in order for the separation process to be economically feasible and more
efficient compared to other separation processes.
Activated carbon. Activated carbons are commonly used adsorbents in the
industry. Their wide range of uses include decolorizing sugar solutions, personnel
protection, solvent recovery, volatile organic compound control, hydrogen purification,
and water treatment [6].
They are formed out of elementary microcrystallites stacked in random orientation. The
manufacturing process consists of the thermal decomposition of carbonaceous raw
materials such as hard and soft woods, rice hulls, refinery residuals, peat, lignin, coals,
coal tars, pitches, carbon black and nutshells, such as coconut, and which is followed by
an activation process [6]. The activation process can be done through a gas or through
chemical activation.
Activation with a gas involves heating in the absence of air at temperatures
around 400-500 °C to get rid of all volatile materials and form small pores [6].
Afterwards, steam at 800-1000 ° C, or other gases such as carbon dioxide or flue gases, is
used for activation. In chemical activation, chemicals such as zinc chloride or phosphoric
acid are used directly with the raw materials to produce activated carbon [6].
Packed beds have granular material of particle size in the range of 0.4-2.4 mm.
Activated carbon cloths are made from cellulose-based woven cloth. They have high
external and internal surface areas and compare to the granular form they have higher
capacity and better kinetic properties [6].

26
Table 1.2 displays the full range of pore sizes of activated carbon. The pore size and the
pore size distribution can be controlled while manufacturing to yield a wide range of
adsorbents with different selectivities and applications. For instance, liquid phase
applications need bigger pore sizes than gas phase applications [6].
Table 1.2: Pore sizes in typical activated carbons [7].
Micropores
Mesopores or
transitional
pores
Macropores
Diameter (nm) <2 2-50 >50
Pore volume
(cm3
/g)
0.15-0.5 0.02-0.1 0.2-0.5
Surface area
(m2
/g)
100-3000 10-100 0.5-0.2
(Particle density 0.6-0.9 g/cm3
; porosity 0.4-0.6)
Carbon molecular sieves (CMS). Carbon molecular sieves are produced from
activated carbon by coating the pore mouths with a carbonized or coked thermosetting
polymer.
This special manufacturing procedure converts amorphous carbons with a very narrow
distribution of pore sizes to effective diameters ranging from 0.4-0.9 nm [6]. Figure 1.2
shows the pore structure of carbon molecular sieves. Chemicals like polyvinylidene
dichloride and phenolic resin or naturally occurring materials such as anthracite or hard
coal are used as raw materials in the manufacturing of these adsorbents [6]. Even though
the adsorptive capacity of CMS is lower than activated carbon, this modification on
activated carbon results in better kinetic properties which lead in turn to better kinetic
selectivity. Carbon molecular sieves are mainly used in the production of high purity
nitrogen from air by pressure swing adsorption.

27
Figure 1.2: Molecular sieve carbons (a) Type CMSN2 with bottlenecks near 0.5 nm formed by coke
deposition on the pore mouth; (b) Type CMSH2 formed by steam activation [6].
Carbonized polymers and resins. Pyrolising resins such as formaldehyde and
highly sulphonated styrene/divinyl benzene macroporous ion exchange resins result in
carbonaceous adsorbents with macro-, meso-, and micro porosity and surface areas up to
1100 m2
/g [6]. Their main application is the removal of organic compounds from water
because these adsorbents are more hydrophobic than granular activated carbon.
Polymeric adsorbents. These synthetic non-ionic polymers are practical for
analytical chromatography applications. The polymer matrix is formed from monomers
that are emulsions polymerized in the presence of a solvent which dissolves the
monomers without swelling the polymer [6].
Their surface areas may reach up to 750 m2
/g. The structure of these polymers along
with the controlled distribution of pore sizes, the high surface areas and the chemical
nature of the matrix all contribute to the selective properties of these adsorbents.
One of the applications of polymeric adsorbents is solute recovery from the
aqueous phase including phenol, benzene, toluene, chlorinated organics, PCB’s,
pesticides, antibiotics, acetone, ethanol, detergents, emulsifiers, dyes, steroids, amino
acids, etc. [6].
Silica Gel. Silica gel is a partially dehydrated polymeric form of colloidal silicic
acid with the formula SiO2.nH2O. Spherical particles with a diameter of 2-20 nm
aggregate to form an adsorbent with pore sizes in the range of 6-25 nm and surface areas
in the range of 100-850 m2
/g [6].

28
Its polar surface consists of mainly SiOH and SiOSi groups. Silica Gel can be used to
adsorb water, alcohols, phenols, amines, etc. by hydrogen bonding mechanisms.
Additionally, it is used in the separation of aromatics from paraffins and the
chromatographic separation of organic molecules [6]. Silica gel has higher adsorption
capacities at low temperatures and moderate water vapor pressure. It may lose activity
through polymerization which involves the surface hydroxyl groups. Table 1.3 shows the
typical properties of adsorbent-grade silica gel.
Table 1.3: Typical properties of silica gel [8].
Physical properties
Surface area (m2
/g) 830
Density (kg/m3
) 720
Reactivation temperature (°C) 130-280
Pore volume (%of total) 50-55
Pore size (nm) 1-40
Pore volume (cm3
/g) 0.42
Adsorption properties Percent by weight
H2O capacity at 4.6 mmHg. 25°C 11
H2O capacity at 17.5 mm Hg. 25 °C 35
O2 capacity at 100 mmHg. -183°C 22
CO2 capacity at 250mm Hg. 25°C 3
n-C4 capacity at 250 mm Hg. 25°C 17
Activated alumina. Activated alumina is a high porous form of aluminum oxide
with the formula Al2O3.nH2O. The surface of activated alumina is both acidic and basic
given the amphoteric nature of aluminum. Compared to silica gel, activated alumina’s
surface is higher in polarity with an area in the range of 250-350 m2
/g [6]. Also, at
elevated temperatures alumina has a higher capacity for water; therefore, it is used as a
desiccant for warm gases such as air, argon, helium, hydrogen, low molecular weight
alkanes (C1-C3), chlorine, hydrogen chloride, sulphur dioxide, ammonia and
fluoroalkanes [6]. Activates alumina is also used in drying of some liquids like kerosene,
aromatics, gasoline fractions and chlorinated hydrocarbons and in chromatography [6].

29
Clay materials. Clays are synthesized from natural deposits. They are formed of
layer silicates which adsorb guest molecules between their siliceous layers causing their
crystals to swell. Fuller’s earth is an activated natural montmorillonite. Acid treatment
can increase its surface area to 150-250 m2
/g. Clay materials are used for re-refining
edible and mineral oils, adsorbing toxic chemicals, removing pigments, etc. [6]. The
cationic forms can adsorb a range of polar and non-polar molecules in the presence of
water. Those layers can be enlarged through ion exchange to form pillared interlayered
clays. The charge compensation cations are replaced by polynuclear metal ion hydro-
complexes which are formed in hydrolyzed solutions of polyvalent metal ions such as
Al(III) or Zr(IV) [6]. The polynuclear cations dehydrate on calcination to create metal
oxide clusters which act as pillars between the clay layers and create spaces of molecular
dimensions [6]. Those pillared clays are used in the separation of oxygen and nitrogen,
and the separation of isomers.
Zeolites. Zeolites are crystalline alumino-silicates. They are called molecular
sieves because they have the ability to separate molecules by their size. There is a huge
variety of natural and synthetic zeolites. Synthetic types A and X, synthetic mordenite
along with their ion exchange varieties are the most used commercially. The zeolite
framework consist of an assemblage of SiO4 and AlO4 tetrahedra joined together in
different regular arrangement with a shared oxygen atom, to form an open crystal lattice
containing pores of molecular dimensions into which sorbate molecules can penetrate [7].
The uniform micropore structure produced by the crystal lattice makes zeolites different
than other microporous adsorbents.
The zeolite framework consists of several tetrahedrals joined together in different
polyhedral arrangements to form secondary units. Figure 1.3 shows some secondary
building units with commonly occurring polyhedral. Each vertex represents a Si or Al
atom while the lines represent the diameters of the oxygen atoms or ions. Each aluminum
atom contributes to a negative charge which must be balanced by a cation through ion
exchange. Those exchangeable cations play a very important role in determining the
adsorptive properties. Si atoms are always more than Al atoms in a given zeolite
framework. The Si/Al ratio determines the adsorptive properties of zeolites.

30
Aluminum rich sieves have higher affinities for water and other polar molecules while
microporous silicas are hydrophobic and adsorb n-paraffins in preference to water.
Figure 1.3: (a) secondary building units. (b) Commonly occurring polyhedral units in zeolite
framework structures [7].
Zeolite A. Figure 1.4 shows a schematic diagram of the zeolite A structure. As
described by Ruthven [7] the structure of a pseudo cell of a zeolite consists of eight unit
cells of type ß (shown in Figure 1.3) located at the corners of a cube and connected
through four membered oxygen rings. This arrangement assembles a large polyhedral α
cage with a free diameter of 11.4 Å. These cells stack together in a cubic lattice to form
three dimensional isotropic channel structure, constricted by eight-membered oxygen
rings. Each pseudo cell contains 24 tetrahedral AlO2 or SiO2 and since the Si/Al ratio is
always close to 1, there are 12 univalent exchangeable cations per cell. Exchanging with
different cations produces zeolites with different selectivities and adsorptive properties.
For example 5A zeolites, produced from exchanging with Ca2+
or Mg2+
, can
accommodate larger molecules than 3A zeolites obtained by potassium exchange.

31
Figure 1.4: Framework structures of zeolite A [7].
Zeolite X and Y. Their structures, as shown in Figure 1.5 below, are formed by a
group of tetrahedrons with the aluminum and silicon atoms at the center and four oxygen
atoms at the vertexes [9]. Groups of tetrahedrons form regular structures of stumped
octahedrons or a sodalite cage, which has 8 hexagonal sides (formed by 6 tetrahedrons)
and 6 square sides (formed by 4 tetrahedrons) [9]. The shape of a sodalite cage is shown
in the Figure 1.6.
Figure 1.5: Tetrahedron [9]
Figure 1.6: Sodalite cage. [9]

32
The basic element of these zeolites X and Y consists of 6 sodalite cages with the
hexagonal faces connected through prisms, Figure 1.7. A network of very small pores,
with an internal diameter of around 7.5Å, leads to cavities inside the zeolite with a mean
diameter of 13Å (Raseev [9]). The internal surface area of the pores is around 600 m2
/g
[10].
Figure 1.7: Framework structures of zeolite X and Y [7].
Zeolite X and Y have the following common formula [9]:
Nan[(Al2O3)n(SiO2)192−n]. mH2O
m ≈ 250-260
n ≈ 48-76 for zeolite Y
≈ 77-96 for zeolite X
The difference between type Y and X zeolites is the Si/Al ratio. Having lower
Si/Al ratio, X zeolites are also less thermally and hydrothermally stable. Each silicon and
aluminum atom is connected to four oxygen atoms. That leaves the silicon atom neutral
while placing a negative charge on the aluminum atom as shown below.
Figure 1.8: Chemical structure of zeolite X and Y [9].

33
1.1.6 Pelletization
Commercial molecular sieve zeolite crystals are small in size and, on their own,
cannot withstand severe conditions and mechanical attrition. Therefore they are produced
in forms of macroporous pellets of suitable size, porosity and mechanical strength.
Nevertheless, the pellet form gives rise to two kinds of resistances: micropore diffusional
resistance of the zeolite crystal itself and the macropore diffusional resistance of the
intracrystalline pores. Reducing the crystal size reduces intracrystalline resistance but it
may also, in turn, increase the diameter of intercrystalline macropores causing the
diffusivity to drop to undesired levels. Reducing the gross particle size reduces
macropore resistance but if the particles are too small, pressure drop might also become
unacceptable. That is why an optimum pellet design balances between macro- and micro-
pore resistances depending on the system designed.
Pellets may be formed in different ways. The most common processes are: extrusion
to form cylindrical pellets, granulation to form spherical particles, and combined
processes of extrusion followed by rolling to form spheres.
A clay material is sometimes added to the pellet in order to bind the crystals and supply
the desired mechanical strength. The binder usually accounts for 10-20% of the final
pellet and sometimes it would be much less than that.
Care must be taken in choosing the binder material as some might have adsorptive
properties and might, as a result, reduce the selectivity as compared to unaggregated
crystals.
1.1.7 Adsorbent selection
A wide variety of adsorbent are available in today’s industry. Choosing the most
appropriate and effective one depends on the properties of this adsorbent compared to the
separation or purification process desired. In order to know whether a certain adsorbent is
suitable for a given separation or purification process, one should first look at the
equilibrium data at the temperature and pressure of interest.
Equilibrium isotherms can be obtained experimentally or can be supplied by the
vendor. Once equilibrium data are interpreted, the kinetic properties of that adsorbent
should be studied.

34
If both equilibrium data and kinetic properties indicate that the given adsorbent can
achieve the desired purity then the next step is to establish a method of regenerating the
adsorbent. Finally the adsorbent should have suitable physical and mechanical properties
to withstand all the process condition including the regeneration step.
1.1.8 Measurement techniques
The following is a brief description of two of the most basic methods of
measuring gas adsorption equilibria on a solid phase [11].
Volumetry/ Manometry. Volumetry was the first method invented to measure the
adsorption of gases on solids. Its basic principle is subjecting a known amount of gas to
an evacuated solid where the sorbate become adsorbed on the surface of the adsorbent
until equilibrium is reached. The amount adsorbed can then be calculated through mass
balance done on the system. The void volume of the adsorbent, the volume that doesn’t
contain any adsorbent, as well as the dead volume in the cell must be taken into account.
Figure 1.9 shows the experimental setup for volumetric measurements of pure gas
adsorption equilibria. It consists of a gas storage vessel connected to an adsorption
chamber through a tube bearing a valve.
A thermostat is setup within both vessels in order to control the temperature. Tubes are
connected to the vessels to supply and evacuate gases as needed. Both temperature and
pressure are monitored through thermometers and manometers respectively. The
adsorbent material being tested should be activated at high temperatures in vacuum to
make sure all pre-adsorption gases are evacuated. The gas chamber is evacuated and a
known amount of gas is loaded. The expansion valve is then opened to allow the gas to
expand to the adsorption chamber where it gets adsorbed on the surface of the adsorbent.
The achievement of constant temperature and pressure indicates that thermodynamic
equilibrium has been reached. From the pressure and temperature the amount of gas
adsorbed can be calculated using an appropriate equation of state.

35
Figure 1.9: Experimental setup for volumetric measurement of pure gas adsorption equilibria [11].
Gravimetry. It is one of the new methods of measuring gas adsorption equilibria
that was made possible due to the development of highly sensitive balances that are able
to measure small relative changes in the weight of the adsorbent sample. The two beam
microbalance is one of the gravimetric techniques used to measure the adsorption of pure
non-corrosive gases on a solid. The schematic diagram shown in Figure 1.10 is the
experimental setup used. Two vessels, one contains the sample and the other contains
ballast, are mounted under the balance and are placed in a thermostat. Gas is supplied and
evacuated through tubes connected to the vessels. A thermostat and a manometer are
mounted on both vessels as well to monitor the temperature and pressure respectively.
The adsorbent sample is mounted inside the microbalance to be activated by evacuation,
heating and flushing with helium. Next the balance must be evacuated before measuring
the adsorbent sample initial weight. After that the gas is administered to the adsorbent
vessel which causes the balance recording to change. This change is not only due to the
adsorption of gas on the sorbent’s surface but also due to the buoyancy effects of the
sample in the surrounding gas. In gravimetry, one can identify the approach to
equilibrium through the data display on the balance. If the mass change is less than some
predefined value in a defined time interval then equilibrium can be assumed.
Temperature, pressure and the final sample weight is recorded. After that the
pressure in increased in sequential steps and the procedure is repeated to get the amount
adsorbed at each pressure. Buoyancy effects must be accounted for.

36
Figure 1.10: Experimental setup for gravimetric measurements of pure gas adsorption equilibria using a
two beam balance [11].
In case of corrosive gases like NH3 or SO2, a single beam balance setup is used,
shown in Figure 1.11, instead of the double beam one. To prevent the corrosive gas from
touching the microbalance, the sorbent is loaded on a suspension rod that hangs freely
inside the adsorbent vessel due to the magnetic field coming from above. Other than that
the procedure of measuring the sample weight is similar to what have been discussed
earlier in the two beam microbalance.
Figure 1.11: Experimental setup for gravimetric measurements of pure gas adsorption
equilibria using a single beam balance [11].

37
1.2 Literature Review
A number of studies exist in literature on the adsorption of hydrocarbons on 13X
zeolites. Those studies contain information on the measurement techniques, adsorption
isotherms and heats of adsorption. For the purpose of this study, adsorption data were
collected from 22 different studies that measured the adsorption of some selected alkanes,
alkenes and aromatics. This section includes a brief description of each of the studies that
were used to get the adsorption data.
Barrer and Sutherland [12] investigated the occlusion of paraffins, including (nC1-
nC8), i-C4, i-C5, neo-C5 and i-C8, and some permanent gases within the crystal lattice of
dehydrated synthetic faujasite (Na2O.Al2O3.2.67SiO2.mH2O).Adsorption measurements
were quantified through a sorption apparatus that comprised both gravimetric and
volumetric sections. Isotherms of the studied species were constructed by plotting the
amount adsorbed vs. the pressure and the differential heats of sorption were evaluated.
Barrer et al. [13] studied the properties of the inclusion complexes of cyclic
hydrocarbons in the structures of faujasites. The adsorption of toluene, benzene,
cyclopentane and cyclohexane were measure and their isotherms were constructed.
Thermodynamic data such as the heat of adsorption and the entropy change were also
measured for the selected hydrocarbons.
Zhdanov et al. [14] measured the adsorption of benzene and n-hexane and their
binary solutions on 10X and 13X zeolites.
Ruthven and Doetsch [15]measured the diffusivity of four hydrocarbons, nC7H16,
C6H12, C6H6 and C6H5.CH3, on 13 X zeolite by the gravimetric technique. The purpose of
the study was to investigate the dependence of diffusivity on concentration and
temperature in such systems. Equilibrium isotherms, Henry’s constant and heats of
adsorption were also measured for these hydrocarbons.
Rolniak and Kobayashi [16] measured the adsorption of pure methane and several
methane-carbon dioxide mixtures on 5A and 13X molecular sieves at elevated pressures
and near ambient temperatures by applying the principles of tracer perturbation
chromatography. The data were correlated by applying the statistical mechanical model
of Ruthven.

38
Hyun and Danner [17] used the static volumetric method to determine the
adsorption equilibria of C2H4, C2H6, i-C4H10 and CO2 and their binary mixtures on 13X
molecular sieves at various temperatures between 273 and 373 K.
Loughlin et al. [18] reported the pure and multi-component adsorption data for the
adsorption of the light n-alkanes, (nC1-nC4), on Linde 5A and 13X pellets in the
temperature range 275-350 K. The intrinsic Henry’s law constant and the heats of
adsorption were extracted from the data using virial isotherm techniques.
Ruthven and Tezel [19] studied the sorption of benzene on NaX zeolites where
they reported an unusual hysteresis effect that was observed from the adsorption
measurements. Measurement studied in this paper was done gravimetrically using a
vacuum microbalance system on a sample of unaggregated NaX crystals.
Ruthven and Kaul [20] measured the equilibrium isotherms and isobars of a series
of aromatic hydrocarbons (benzene, toluene, tetramethylbenzene, dimethylnaphthalene,
and anthracene) on NaX crystal zeolites. Henry’s constants and the heats of adsorption
were also reported in the study.
Salem et al. [21] measured the adsorption equilibria of argon, nitrogen and
methane on 13X molecular sieves and activated carbon using a microbalance at five
temperatures over a wide pressure range. The equilibrium isotherm data were used to
calculate the absolute isotherms using equations of state for a real gas.
Da Silva and Rodrigues [22] measured the single adsorption equilibrium
isotherms of propylene and propane and their mass-transfer kinetics on 13X and 4A
zeolite pellets using gravimetry and zero length column techniques, respectively. The
experimental equilibrium isotherm data obtained were fitted by the Toth isotherm
equation.
Wang et al. [23] measured the adsorption of some organic compounds, benzene,
toluene, o-xylene, p-xylene, and m-xylene, on the activated carbon, silica gel and 13X
zeolite by the gravimetric adsorption method. The equilibrium isotherm data obtained
were fitted by the Freundlich equation.
Pinto et al. [24] studied the adsorption of toluene and nitrogen on different
composite adsorbent materials to study the effect of the supporting process in the

39
adsorption capacity of those materials. Three activated carbons, one zeolite and one
pillared clay were supported in polyurethane foam to form the composite material.
Lamia et al. [25] measured the adsorption equilibrium isotherms of propylene,
propane, and isobutane on 13Xzeolite pellets over a temperature range from 333 K to 393
K and pressure up to160 kPa using the gravimetric method. The adsorption equilibrium
isotherm data were fitted by the Toth equation. The aim of this study was to investigate
the ability of iso-butane to act as a desorbent of the propane/ propylene mixture over 13X
zeolite in a simulated moving bed. The heats of adsorption at zero coverage for
propylene, propane, and iso-butane were also measured.
Lamia et al. [26] measured the adsorption equilibrium of 1-butene over 13X
zeolite by the gravimetric method at temperature of 333, 353, 373 and 393 K. The
experimental adsorption data were fitted by the Toth equation. The heat of adsorption at
zero coverage and the maximum loading capacity of 1-butene were also measured.
1.3 Deliverables
Modeling experimental adsorption equilibrium data is a way of theoretically
predicting unmeasured adsorption equilibrium data for materials of the same species. The
most commonly used models in adsorption equilibria use the concept of surface coverage
or micropore volume filling and were either derived from a kinetic or a thermodynamic
point of view. A new idea was put forward to model adsorption data that is different from
all traditional models. Abouelnasr and Loughlin [27] proposed a model based on the
Gaussian cumulative frequency distribution principles, which has been used before to
model energy sites rather than adsorption sites [27].
In this study, the Gaussian model is used to model data on the adsorption
of hydrocarbons on 13X zeolites; the data has been collected from previous
published work in literature. The scope will cover selected sorbates from
alkanes, alkenes and aromatics. The parameters of the model will be determined
for each group of hydrocarbons by fitting the experimental data by the Gaussian
equation. Heats of adsorption at a constant θ of 50% will be determined for each
species.

40
1.4 Thesis Outline
• Chapter1: thesis introduction. Includes background information, literature review
and thesis deliverables.
• Chapter 2: theoretical background and model derivation.
• Chapter 3: modeling the adsorption of alkanes over 13X zeolite by the Gaussian
model.
• Chapter 4: modeling the adsorption of alkenes over 13X zeolite by the Gaussian
model.
• Chapter 5: modeling the adsorption of aromatics over 13X zeolite by the Gaussian
model.
• Chapter 6: Conclusion.

41
CHAPTER 2: Theoretical Background and Model Derivation
2.1 Adsorption Equilibrium Theory
2.1.1 Langmuir theory
Adsorption equilibria have been studied since the beginning of the 20th
century.
The first basic theory of adsorption was derived by Langmuir back at 1918. This theory
assumes an ideal surface on which surface adsorption occurs, and it is deduced from a
kinetic point of view. Three main assumptions of this theory are [5]:
1- Homogenous surface, meaning that the adsorption energy is constant across the
surface on each site.
2- One molecule only can be adsorbed on each site.
3- Adsorption occurs on definite, localized sites.
The well known Langmuir isotherm,
𝜃 =
𝑏𝑃
1+𝑏𝑃
2.1
is derived originally from equating the rate of adsorption on an occupied site, eq. 2.2, to
the rate of desorption on an occupied site, eq. 2.3:
𝑅𝑎 =
𝛼𝑃
�2𝜋𝑀𝑅𝑔𝑇
(1 − 𝜃) 2.2
𝑅𝑑 = 𝑘𝑑𝜃 = 𝑘𝑑∞𝑒
−(
𝐸𝑑
𝑅𝑔𝑇
)
𝜃 2.3
The term �
P
�2πMRgT
� in equation 2.2 is the rate of striking the surface, Rs, in mole per
unit time per unit area, obtained from the kinetic theory of gases [5]. This term is
multiplied by a sticking coefficient, α, to account for non ideal sticking on a non ideal
surface. The term is also multiplied by (1-θ) which is the fraction of empty sites to
finally yield the rate of adsorption given by equation 2.2.
The rate of desorption in equation 2.3 is the equal to kd, the rate of desorption from a
fully covered surface, multiplied by θ, the percent coverage. Ed is the activation energy

42
for desorption, kd∞ is the rate constant for desorption at infinite temperature and b is the
Langmuir constant given by:
𝑏 =
𝛼exp(𝑄 𝑅𝑔𝑇)
⁄
𝑘𝑑∞�2𝜋𝑀𝑅𝑔𝑇
2.4
Here Q is the heat of adsorption and is equal to the activation energy for
desorption, Ed.This equality follows the assumption that at equilibrium, the rate
of bombardment of molecules onto the surface is equal to the rate of desorption
of molecules from the surface and, hence, zero accumulation occurs at
equilibrium.
2.1.2 Gibbs thermodynamic theory [5]
Another theory was proposed from a thermodynamic point of view. Gibbs used
the principles of classical thermodynamics of the bulk phase and applied it to the
adsorbed phase.
In this analogy the volume is replaced by the area and the pressure is replaced by what is
called the spreading pressure, π. The result is the Gibbs isotherm equation:
�
𝑑𝜋
𝑑𝑙𝑛𝑃
�
𝑇
=
𝑛
𝐴
𝑅𝑔𝑇 2.5
Given an equation of state that relates the spreading pressure to the number of
moles in the adsorbed phase, an isotherm can be produced that expresses the number of
moles adsorbed in terms of pressure. Two examples are the linear isotherm and the
Volmer isotherm.
Linear isotherm:
𝑛
𝐴
= 𝐾(𝑇)𝑃 2.6
𝐾(𝑇) =
𝐶(𝑇)
𝑅𝑔𝑇
2.7
where C (T) is some function of temperature and K (T) is called Henry’s constant.
Volmer isotherm:
𝑏(𝑡)𝑃 =
𝜃
1−𝜃
exp �
𝜃
1−𝜃
� 2.8
𝑏(𝑇) = 𝑏∞𝑒𝑥𝑝 �
𝑄
𝑅𝑔𝑇
� 2.9

43
The linear isotherm is applied to dilute systems where the adsorbed molecules act
independently from each other. The Volmer isotherm on the other hand takes into
account a finite size of the adsorbed molecules. Nevertheless, the Volmer isotherm still
does not take into account the mobility of the adsorbed molecules. This factor can be
included by using a different equation of state, one that includes the co-volume term and
the attractive force term.
An example is the following van der Waals equation:
�𝜋 +
𝑎
𝜎2� (𝜎 − 𝜎0) = 𝑅𝑔𝑇 2.10
σ is the area per unit molecule adsorbed.
The resulting isotherm is:
𝑏𝑃 =
𝜃
1−𝜃
𝑒𝑥𝑝 �
𝜃
1−𝜃
� exp(−𝑐𝜃) 2.11
𝑏 = 𝑏∞𝑒𝑥𝑝 �
𝑄
𝑅𝑔𝑇
� 2.12a
𝑐 =
2𝑎
𝑅𝑔𝑇𝜎0
=
𝑧𝑤
𝑅𝑔𝑇
2.12b
where z is called the coordination number and is given the values 4 or 6 depending on the
packing of molecules, and w is the interaction energy between the adsorbed molecules.
This isotherm is called the Hill-deBoer Isotherm and is used in cases where there
is mobile adsorption and lateral interaction among adsorbed molecules. Eliminating the
first exponential factor from this isotherm presents the case where there is no lateral
interaction among molecules to result in what is called the Fowler Guggenheim equation
or the quasi approximation isotherm:
𝑏𝑃 =
𝜃
1−𝜃
exp(−𝑐𝜃) 2.13

44
2.1.3 Statistical thermodynamic theory
In a similar manner different isotherms were proposed from different equations of
state. Each of these isotherms describes a unique type of adsorption depending on the
equation of state used.
Models were also derived using statistical thermodynamics. Multisite occupancy
model of Nitta et al. [28] is an example:
𝑛𝑏𝑃 =
𝜃
(1−𝜃)𝑛
𝑒𝑥𝑝 �−
𝑛𝑢
𝑘𝑇
𝜃� 2.14
𝑏 =
𝑗𝑠𝜉
𝑗𝑔
Λ3
𝑘𝑇
exp �
𝜀
𝑘𝑇
� 2.15
where b is the affinity constant given by the previous equation, Λ is the thermal de
Broglie wavelength, js is the internal and vibrational partition functions of an adsorbed
molecule, jg is the internal partition function of gas phase, ε is the adsorption energy per
molecule for adsorbate-adsorbent interaction, and u is the molecular interaction
parameter for adsorbate– adsorbate interaction.
One of the important models of adsorption also, developed by Suwanayuen and
Danner [29], is the vacancy solution model. The system is assumed to consist of two
solutions, the gas phase and the adsorbed phase, where both differ in their densities. The
isotherm equation was derived by substituting the following equation of state (for species
v) into the Gibbs isotherm equation:
𝜋 = −
𝑅𝑔𝑇
𝜎𝑣
ln(𝛾𝑣𝑥𝑣) 2.16
where γ is the activity coefficient and x is the mole fraction.
The result is the following isotherm:
𝑃 = �
𝐶𝜇𝑠
𝐾
𝜃
1−𝜃
� �ΛIv
1−(1−ΛvI)θ
ΛIv+(1−ΛIv)θ
� 𝑒𝑥𝑝 �−
Λ𝑣𝐼(1−Λ𝑣𝐼)𝜃
1−(1−Λ𝑣𝐼)𝜃
−
(1−ΛIv)θ
ΛIv+(1−ΛIv)θ
� 2.17
where K is the Henry constant; Cμs is the maximum adsorbed concentration.
𝜃 =
𝐶𝜇
𝐶𝜇𝑠
2.18

45
2.1.4 Empirical isotherm equations
Equations that were found to best describe data of hydrocarbon adsorption are
empirical isotherm equations [5]. The earliest of these isotherms was used mostly by
Freundlich (1932), hence was called by his name:
𝐶𝜇 = 𝐾𝑃1/𝑛
2.19
where Cμ is the concentration of the adsorbed species; K and n are temperature
dependent.
More empirical equations were found later such as the Sips equation (Freundlich-
Langmuir), Toth equation, Unilan equation, Keller et al., Dubinin-Radushkevitsh,
Javonovish equation and Temkin. Braunauer; Emmett and Teller developed an empirical
equation that describes sub-critical adsorbates where multi-layer adsorption takes place.
The BET theory was published in 1938 and was modified later on by other researchers.
Nevertheless the original BET theory remained the most important equation to describe
mesoporous solids adsorption [5].
𝑉
𝑉𝑚
=
𝐶𝑃
(𝑃0−𝑃)[1+(𝐶−1)(𝑃 𝑃0
⁄ )]
2.20
2.2 Henry’s Law
Physical adsorption does not involve association or dissociation of molecules
hence the molecular state of the adsorbent is preserved. If physical adsorption is to occur
on a uniform surface at sufficiently low concentrations of the adsorbed phase the
molecules will act as if they are isolated from their nearest neighbor. As a result, the
relationship between the adsorbed and fluid phase concentrations will be linear. The
constant of proportionality is the adsorption equilibrium constant and it is analogous to
Henry’s constant. Similarly, the equilibrium relation is analogical to Henry’s Law. As
shown in the following equation the adsorption equilibrium constant (Henry’s constant)
can be expressed in terms of pressure or concentration:
q = Kc or q = K′ P 2.21
where q and c are the adsorbed and fluid phase concentrations, respectively.

46
Henry’s constant obeys the vant Hoff equation for temperature dependence:
𝑑𝑙𝑛𝐾′
𝑑𝑇
=
∆𝐻0
𝑅𝑇2
,
𝑑𝑙𝑛𝐾
𝑑𝑇
=
∆𝑈0
𝑅𝑇2
2.22
where ∆H0 and ∆U0 are the differences in enthalpy and internal energy, respectively,
between adsorbed phase and gaseous phase. The previous equations can be integrated,
with the assumption that the heat capacity between the phases is negligible, to yield:
𝐾′
= 𝐾0
′
𝑒−∆𝐻0/𝑅𝑇
, 𝐾 = 𝐾0𝑒−∆𝑈0/𝑅𝑇
2.23
2.3 The Gaussian model
A new idea was put forward to model adsorption data that is different from all
traditional above. Abouelnasr and Loughlin [27] proposed a model based on the Gaussian
cumulative frequency distribution principles, which has been used before to model
energy sites rather than adsorption sites.
According to Abouelnasr and Loughlin [27], adsorption phenomena should be
very well described by the Gaussian normal probability distribution function. This is
because adsorption is the probability that a molecule gets adsorbed on a surface and it
depends upon the following probabilities:
1- The molecule collides with a site on that surface.
2- The site is available.
3- The kinetic energy of the molecule is low enough to prevent it from escaping.
In their paper, Abouelnasr and Loughlin [27] used the adsorption data of methane
on 5A zeolite to test the model. The data were collected from six studies to get a total of
24 isotherms that were fitted to the new model.
Figure 2.1 shows the similarity between the shape of adsorption isotherm of methane
on 5A zeolite, θ vs. P, and the Gaussian cumulative frequency distribution function [27].
This similarity establishes that the adsorption process follows the Gaussian cumulative
distribution [27].

47
Figure 2.1: (a) Isotherm for methane on 5A zeolite at 194.5 K. data are from Stroud et al. [30] a value
for qmax of 9 g/100 gZ is used in calculating θ. (b) cumulative distribution function for the standard normal
distribution [27].
Abouelnasr and Loughlin [27] stated the following assumptions for the new
isotherm:
1. Molecules in the gas phase have a Maxwell-Boltzmann distribution of velocities
and energies.
2. All adsorption sites are equivalent.
3. The adsorbed phase inside the micropores is assumed to be a condensed liquid
state even though it might have different properties.
4. Adsorption sites are filled to saturation at maximum adsorption.
5. There is no interaction between molecules that are adsorbed on adjacent sites.

48
2.3.1 Model derivation
First a normal distribution variable, Z, is defined as:
𝑍 =
log(𝑃)−log(𝑃𝐿𝑀)
𝜎
2.24
where PLM is the log mean pressure which is defined in this case as the pressure at 50% of
the maximum loading or P50 and σ is the standard deviation for the entire isotherm. Note,
since this chapter is a literature review, log base 10 is used as the original papers were
written in this fashion. However, from chapter 3 onwards in this thesis, all calculations
are done using ln base e as this is the logical interpretation of the Gaussian isotherm. Φ
(Z) is the cumulative distribution function for the standard normal distribution where it
represents the area to the left of Z under the bell shaped curve [31]. The function, Φ (Z),
is defined by:
Φ(𝑍) =
1
√2𝜋
∫ 𝑒−𝑍2 2
⁄
𝑑𝑍
𝑍
−∞
2.25
Rearranging equation 2.24 yields:
𝑍 = 𝑙𝑜𝑔 �
𝑃
𝑃50
�
1
𝜎
2.26
In this model the cumulative distribution function, Φ (Z), corresponds to θ or
q/qmax.
Φ �
log(𝑃)−log(𝑃𝐿𝑀)
𝜎
� = 𝜃 2.27
From the definition of Φ (Z), θ can be written as:
𝜃 =
𝑞
𝑞𝑚𝑎𝑥
=
1
√2𝜋
∫ 𝑒−𝑍2 2
⁄
𝑑𝑍
log�
𝑃
𝑃50
�
1 𝜎
⁄
−∞
2.28
Equation 2.28 is the Gaussian isotherm model equation. The value of this integral
is tabulated for different values of Z. NORMSDIST and NORMSINV are functions in
EXCEL that may be used to calculate Φ and Φ-1
. From equation 2.28 we can see that
three parameters, qmax, the standard deviation σ and the 50% adsorbate loading pressure
P50 are needed to specify the isotherm.
Taking the inverse of the cumulative equation, equation 2.27, gives:
�
log(𝑃)−log(𝑃50)
𝜎
� = Φ−1
(𝜃) 2.29

49
Rearranging equation 2.29 gives:
log(𝑃) = 𝜎Φ−1
(𝜃) + log(𝑃50) 2.30
A plot of log (P) vs. Φ-1
should give a straight line with a slope equal to the standard
deviation and a y-intercept equal to log (P50).
The isostere relation at constant loading describes the relation between
the pressure at 50% of the maximum loading and the temperature [32]:
𝑃50 = 𝑎√𝑇𝑒−∆𝐻50 𝑅𝑇
⁄
2.31
Here, a represents the pre exponential factor and (-ΔH50) is the heat of adsorption at 50%
loading. The effect of the square root may be neglected so that the plot of ln P vs. 1/T
should yield a straight line with (-ΔH50 /R) as the slope.
At low adsorption loadings, Henry’s law region is:
𝐾𝐻 = lim𝑝→0 �
𝑑𝑞
𝑑𝑃
� 2.32
KH is Henry’s law constant.
Given that the adsorption is homogenous, q may be replaced by (θqmax) and P by
P50* (P/P50) to give:
𝐾𝐻 =
𝑞𝑚𝑎𝑥
𝑃50
lim𝑃→0
𝑑𝜃
𝑑(𝑃/𝑃50)
2.33
Methane adsorption on 5A zeolite is considered to be homogenous and hence KH may be
calculated from the slope of the plot of θ vs. P/P50.
As stated earlier, the model was tested by collecting data for methane-5A zeolite
from six different studies, shown in the Table 2.1. A total of 24 isotherms were used with
a temperature range of 185 to 308 K.
Table 2.1: Adsorption studies of methane on 5A zeolite [27].
Reference Adsorption Temperature (K)
Loughlin [33] 185, 230, 273
Loughlin et al. [18] 275, 300, 325, 350
Mentasty et al. [34] 258, 273.3, 283, 298
Rolnaik and Kobayashi [16] 288, 298, 308
Stroud et al. [30] 194.5, 218, 233, 253, 273, 288, 300
Zeuch et al. [35] 273, 298, 308

50
A previous study done by Loughlin and Abouelnasr [36] found that qmax, the
maximum zeolite loading, was found to be 8±1 g/100g Z at reduced temperatures above a
Tr of 0.83. The latter value is the reduced critical temperature for the adsorbed phase also
found from the same study.
Using a value of 9 g /100 gZ for qmax, the following results were achieved:
Figure 2.2 shows the linearized isotherms for this system according to equation 2.30. The
parallel straight lines indicate an agreement with the linear fit.
The slopes range from 0.83 to 1.13 with a mean of 0.98 and a standard deviation of
0.088. The standard deviation, σ, represented by the slopes is taken to be 1 for all
isotherms.
In Figure 2.3, log (P/P50)1/σ
is plotted against Φ-1
according to equation 2.26. All
24 normalized isotherms are overlaid on a single line taking P50 and σ separately for each
isotherm. Data are clearly well represented by this straight line as can be seen in the
figure.
Another representation for all the data in the 24 isotherms are shown in the S
shaped curve on Figure 2.4. The plot is similar to the plot in Figure 2.1 which is for one
isotherm at 194.5 K. all data fall perfectly on the S shaped curve in agreement with
equation 2.27.
Figure 2.2: Linearized isotherms for methane adsorption on 5A zeolite [27].

51
Figure 2.3: Data from 24 methane isotherms overlaid on a single normalized linear isotherm [27].
Figure 2.4: Data from 24 methane isotherms, overlaid on a single normalized isotherm graph [27].

52
According to equation 2.31, neglecting the square root effect, a plot of lnP50 vs.
1/T should have a slope equal to (-ΔH50 /R), the heat of adsorption at 50% loading
providing qmax is constant as in the case of methane. Abouelnasr and Loughlin found a
value of 4.97 kcal/mole for the heat of adsorption [27] and compared it to values reported
in a previous study by Loughlin et al. [18]. The values reported were in the range of 4.5-
5.12 kcal /mole, which is quiet close to the one calculated by the Gaussian model.
In their paper, Abouelnasr and Loughlin [27] also compared the Gaussian
isotherm to two other isotherms, the Langmuir and multi-site Langmuir. Two isotherms
were chosen, at 194.5 K and 308 K, from the 24 ones used in this study. Figure 2.5
displays the two isotherms each plotted with the three models. The figures suggests that
at 194.5 K both the Langmuir and the MSL models over predict q at high pressures and
under predict q at low pressures. At 308 K, both the Gaussian and the MSL model agree
with the experimental data unlike the Langmuir model which falls off the models and the
data. Figure 2.6 displays the predictions from the Gaussian model and the experimental
data from all 24 isotherms, each plotted separately. The Gaussian model seems to be in a
very good agreement with the data for most of the isotherms.
Figure 2.5: Two isotherms of methane adsorption, (194.5K from [30]and 308 K from [35]) [27].

53
Figure 2.6: Experimental data for 24 isotherms, compared to prediction from Gaussian model [27].
2.3.2 Maximum saturation loading
The maximum saturation loading, or qmax, is one of the three parameters needed to
specify the isotherms in the Gaussian model. Loughlin and Abouelnasr [36] implemented
the Rackett equation combined with crystallographic data for the zeolite in order to evaluate
the saturation loading for subcritical n alkanes on 5A zeolites. The saturation density
model was derived by starting with the first principle relation:
𝑞𝑚𝑎𝑥 �
𝑔
100 𝑔𝑍
� = 100
𝜌𝑠𝑎𝑡𝜀𝑍
𝜌𝑍
2.34
In cases where there is a fraction of binder in the pellet, ω, the following relation is used
to relate q*max based on adsorbent to qmax based on crystal.
𝑞 ∗𝑚𝑎𝑥 �
𝑔
100 𝑔𝑍
� = 𝑞𝑚𝑎𝑥𝜔 2.35
The saturation density for subcritical liquids is calculated using the modified Racket
equation:
𝑉𝑠𝑎𝑡 =
1
𝜌𝑠𝑎𝑡
= �
𝑅𝑇𝐶
𝑃𝐶𝑀𝑊
� 𝑍𝑅𝐴
�1+(1−𝑇𝑟)0.2857�
2.36
where Zra is a constant specified for the modified Rackett equation; values are listed in
the paper by Spencer and Danner [37].

54
Combining equations 2.34 and 2.36 gives:
𝑞𝑚𝑎𝑥 �
𝑔
100 𝑔𝑍
� = 100
𝜀𝑍
𝜌𝑍
�
𝑃𝐶𝑀𝑊
𝑅𝑇𝐶
� 𝑍𝑅𝐴
−�1+(1−𝑇𝑟)0.2857�
2.37
As for supercritical adsorption on alkanes it is important to note that the reduced
critical temperature for the adsorbed phase, TCAR, is not taken as 1. This is because the
critical region for the adsorbed phase starts earlier than in the case of vapor-liquid
systems. According to Loughlin and Abouelnasr [36], the value of TCAR is taken to be
0.975 for alkanes C3 to C18, whereas for methane and ethane the values of TCAR are taken
as 0.83 and 0.96 respectively. Beyond these subcritical temperatures the theoretical value
of qmax suggested by Loughlin and Abouelnasr [36] was 8±1 g /100gZ.
2.3.3 Predicting adsorption data by the Gaussian model
Using the Gaussian model, Abouelnasr and Loughlin [38] developed predictive
criteria for supercritical n alkane adsorption data on 5A zeolite. Adsorption data for nC1
through nC12 was collected from 18 different studies. A total of 63 isotherms were used
to test the Gaussian model. Again, three parameters are needed to specify the isotherm,
qmax, P50, and σ. Abouelnasr and Loughlin [38] followed specified criteria of choosing the
participating isotherms in this study. Isotherms were compared with each other and
screened to delete any inconsistent data that might have resulted due to capillary
condensation effects. Isotherms were also deleted if they did not follow the majority
pattern or if they crossed other isotherms. An example would be the data for nC10 and
nC12 as shown in Figure 2.7. The darker lines in the figure are misplaced compared to the
rest of the isotherms. Those isotherms belong to nC10 and nC12 and they are studied
separately due to their inconsistency [38]. The isotherm region where θ ≤ 0.01 was
truncated as the Gaussian model does not apply near Henry’s Law region.

55
Figure 2.7: Isotherms nC1 through nC8 compared to isotherms nC10 and nC12 [38].
In order to find the value of P50 and σ a regression analysis is done. According to
equation 2.26, a plot of log P vs. Φ-1
should yield a slope equal to σ and an intercept
equal to log P50. Equation 2.26 can be written in terms of reduced pressure as well with
no change since the critical pressure will cancel from both sides of the equation. Figure
2.8 shows the linearized isotherms from which the parameters are derived for each
isotherm. It was found that the average value of sigma is 0.96 with a standard deviation
of 0.127 [38]. The regression value started at 0.976 with an average of 0.996 and a
standard deviation of 0.005 [38]. This analysis strongly indicates that the model is a
strong fit for the data.
Figure 2.9 overlays all isotherms (nC1 through nC10) on a single characteristic plot
of θ vs. (Pr /P50)1/σ
. All data points fall perfectly on the S shaped curve, also indicating
that the model shows a good representation of the data. In Figure 2.10 n-pentane data
were laid over the Gaussian model; both were in a very good agreement.
The isosteres for 50% loading of nC1 through nC10 were plotted in Figure 2.11.
The slopes represent the heat of adsorption at 50% loading; summarized in Table 2.2.

56
Figure 2.8: Linearized isotherms for nC1 through nC8 [38].
Figure 2.9: Normalized isotherms of nC1 through nC10 [38].

57
Figure 2.10: Isotherms of n-Pentane overlaid with Gaussian isotherm model [38].
Figure 2.11: Isosteres for 50% loading for nC1 through nC10 [38].

58
Table 2.2: Heats of adsorption at 50% loading
Carbon Number
(-ΔH50)
kcal/mole
1 5.0
2 7.1
3
4 11.9
5 13.7
6 15.1
7
8 22.1
10 30.8
Figure 2.12: Heats of adsorption at 50% loading according to Table 2.2 (dark squares) [38].
The following equation for the heat of adsorption was derived from Figure 2.12 as
the best fit equation.
(−∆𝐻50) 𝑘𝑐𝑎𝑙 𝑚𝑜𝑙
⁄ = �
5, 𝑛 = 1
7.1, 𝑛 = 2
6.07 exp(0.16𝑛), 3 ≤ 𝑛 ≤ 10
2.38
Similarly a best fit equation was derived for the pre-exponential factor for the
isosteres, A:
𝐴 𝑃𝑐 = exp(0.0021𝑛3
+ 0.15𝑛2
− 0.76𝑛 + 7.46)
⁄ 2.39
where Pc is the critical pressure and n is the carbon number.

59
Equations 2.38 and 2.39 are used along with equations 2.40 and 2.41 in order to use the
Gaussian model in the predictive mode [38]:
𝑞 = 9 𝑁𝑂𝑅𝑀𝑆𝐷𝐼𝑆𝑇 �
𝑙𝑜𝑔𝑃−𝑙𝑜𝑔𝑃50
𝜎
� 2.40
𝑃𝑟,50 =
𝐴
𝑃𝑐
𝑒∆𝐻50/𝑅𝑇
2.41
NORMSDIST is an EXCEL function as mentioned earlier. 9 in equation 2.40 is the value
of qmax for the supercritical n alkane adsorption on 5A zeolite system.
Abouelnasr and Loughlin [38] chose n-pentane to predict its isotherm using the
Gaussian model and compare it to the data available, as shown in Figure 2.13.
Figure 2.13: Predicted isotherms of n-pentane overlaid with adsorption data [38].
The Gaussian model is an excellent fit to the data proving its validity. Abouelnasr
and Loughlin [38] also predicted isotherms for n-decane at temperatures that have not
been measured before. Figure 2.14 shows the predicted isotherms for n-decane at Tr
=1.01 and 1.08.

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